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A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing

Author

Listed:
  • Ibrahim Mohammed Sulaiman

    (Institute of Strategic Industrial Decision Modelling (ISIDM), School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Sintok 06010, Malaysia)

  • Aliyu Muhammed Awwal

    (Department of Mathematics, Faculty of Science, Gombe State University (GSU), Gombe 760214, Nigeria
    GSU-Mathematics for Innovative Research Group, Gombe Srare University (GSU), Gombe 760214, Nigeria)

  • Maulana Malik

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia (UI), Depok 16424, Indonesia)

  • Nuttapol Pakkaranang

    (Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand)

  • Bancha Panyanak

    (Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

Nonlinear systems of equations are widely used in science and engineering and, therefore, exploring efficient ways to solve them is paramount. In this paper, a new derivative-free approach for solving a nonlinear system of equations with convex constraints is proposed. The search direction of the proposed method is derived based on a modified conjugate gradient method, in such a way that it is sufficiently descent. It is worth noting that, unlike many existing methods that require a monotonicity assumption to prove the convergence result, our new method needs the underlying function to be pseudomonotone, which is a weaker assumption. The performance of the proposed algorithm is demonstrated on a set of some test problems and applications arising from compressive sensing. The obtained results confirm that the proposed method is effective compared to some existing algorithms in the literature.

Suggested Citation

  • Ibrahim Mohammed Sulaiman & Aliyu Muhammed Awwal & Maulana Malik & Nuttapol Pakkaranang & Bancha Panyanak, 2022. "A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2884-:d:886242
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    References listed on IDEAS

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    1. Mohammed Yusuf Waziri & Jamilu Sabi’u, 2015. "A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-8, September.
    2. Anton Rodomanov & Yurii Nesterov, 2021. "New Results on Superlinear Convergence of Classical Quasi-Newton Methods," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 744-769, March.
    3. Rivaie, Mohd & Mamat, Mustafa & Abashar, Abdelrhaman, 2015. "A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1152-1163.
    4. Awwal, Aliyu Muhammed & Kumam, Poom & Abubakar, Auwal Bala, 2019. "Spectral modified Polak–Ribiére–Polyak projection conjugate gradient method for solving monotone systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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    Cited by:

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